Heat-kernels and maximal L-P-L-q-estimates: The non-autonomous case

Authors
Hieber, M Monniaux, S
Citation
M. Hieber et S. Monniaux, Heat-kernels and maximal L-P-L-q-estimates: The non-autonomous case, J FOURIER A, 6(5), 2000, pp. 467-481
Citations number
22
Categorie Soggetti
Mathematics,"Engineering Mathematics
Journal title
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
ISSN journal
10695869 → ACNP
Volume
6
Issue
5
Year of publication
2000
Pages
467 - 481
Database
ISI
SICI code
1069-5869(2000)6:5<467:HAMLTN>2.0.ZU;2-W
Abstract
In this paper, we establish maximal L-p - L-q estimates for non-autonomous parabolic equations of the type u'(t) + A(t)u(t) = f(t), u(0) = 0 under sui table conditions on the kernels of the semigroups generated by the operator s -A(t), t is an element of [0, T]. We apply this result on semilinear prob lems of the form u'(t) + A(t)u(t) = f(t, u(t)), u(0) = 0.